Pharmac. Ther. Vol. 49, pp. 311-327, 1991

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CIRCADIAN RHYTHMS: PRINCIPLES A N D MEASUREMENT P. H. REDFERN,* J. M. WATERHOUSEt a n d D. S. MINORS~' *School of Pharmacy and Pharmacology, University of Bath, Bath BA2 7A Y, U.K. #Department of Physiological Sciences, University of Manchester, Manchester, U.K. Abstract--The physiological basis of rhythmic processes is explained, and the influenceof rhythmicity on pathological processes and pharmacological responses is outlined. Methods of data collection and analysis are described, and the importance of taking account of, and even exploiting, rhythmicity in experimental design is discussed. CONTENTS 1. Introduction 2. The 'Black Box'--A General Description of Circadian Rhythms 3. Opening the Box--Attempts to Describe the Details of Circadian Rhythms 3.1. Effectormechanisms---changesin homeostatic 'set-points' 3.2. Circadian rhythms in pathways 3.3. The internal clock 3.4. Inside the SCN 4. Collecting Data for Circadian Rhythm Studies 4.1. Frequency of sampling 4.2. Combining and smoothing results 5. AssessingRhythms with a 24 hr Period 5.1. Analysis of variance 5.2. Cosinor analysis 5.3. Interpreting changes in rhythm parameters as assessed by cosinor analysis 5.3.1. Change of amplitude 5.3.2. Change in acrophase 5.4. Alternatives to the single cosine curve 5.5. Assessing the time of maximum effect of an experimental procedure 6. Can We Ignore Circadian Rhythms? References

1. I N T R O D U C T I O N In both experimental and clinical pharmacology, time of day is not generally considered as a factor likely to influence the outcome significantly. If time of day is considered, the experiment is likely to be designed so as to eliminate or minimize any supposed temporal influence. In recent years, in the wake of a growing awareness of the ubiquity of regular temporal variation in physiological processes (Minors and Waterhouse, 1981; Moore-Ede et al., 1982; Wever, 1979), interest in time-dependent variation in pharmacological responses has grown. It has become increasingly apparent that the timing of drug administration, especially in relation to time of day, can profoundly influence the observed response. The realization has not only led to a better understanding of the need, when designing experiments or clinical dosing schedules, to control the time of day at which a drug is adminis311

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tered, but also---more positively--has opened up the possibility of exploiting time-dependent differences in response both clinically and experimentally. In the next decade the advent of more sophisticated drugdelivery systems is likely to enable us to optimize these temporal factors. It is therefore opportune to consider the basis of the phenomenon of time-related changes in responsiveness to drugs, and to consider ways of measuring and describing the phenomenon. Consider first the following examples: (i) Postoperatively, it is common to infuse heparin to reduce the chances of blood-clot formation. If heparin is infused at a constant rate, the normal procedure, this can be too high in the evening, so that the chance of spontaneous hemorrhage becomes high, and too low in the morning after sleep, so that the chance of clot formation is still too high (Decousus et al., 1985). This situation arises because there are normally daily rhythms of platelet

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aggregation and fibrinolysis that are phased such that the coagulation-fibrinolytic system is biased slightly towards coagulation just after waking and towards hemorrhage during the evening (Brezinski et al., 1988; Grimando et al., 1988). (ii) In healthy subjects there is a daily rhythm in airway resistance, highest values being found in the night. This rhythm is particularly pronounced in many asthmatic patients, producing most wheeziness and dyspnoea at or about the hours of sleep; in consequence, the frequency of self-administration of bronchodilators by inhalers is highest at night (Barnes, 1989; Muers, 1984; Smolensky et al., 1986). (iii) The same dose of drug can have different kinetics and efficacy according to the time of day it is administered. For example the time-course of the plasma concentration of indomethacin shows a sharper rise, higher peak and more rapid decline after morning administration than after the same dose administered in the evening (Clench et al., 1981). Also the same dose of local anesthetic can be effective for different lengths of time according to the time of administration (for reviews see Markiewicz, 1984; Marks et al., 1985; Reinberg and Smolensky, 1982; Reinberg et al., 1985). The kinetic effects reflect rhythms of intestinal absorption, liver metabolism and renal excretion and the altered efficacy depends partly upon changes in the number and properties of tissue receptors which in turn affect tissue susceptibility to the drug. As these examples show, time can be important in the disease process, its diagnosis and treatment. In healthy subjects also, the concept that physiological and biochemical variables are controlled at fixed and unvarying values is an outdated one. In this account we will outline and explain the rhythmic processes that are found in health as well as describe some of the methods that can be used to describe them quantitatively. 2. THE 'BLACK B O X ' - - A G E N E R A L DESCRIPTION OF CIRCADIAN RHYTHMS Life has evolved in, and adapted to, a rhythmic environment. With the exception of creatures that live in the depths of the oceans, or in the deepest recesses of caves, all living things are influenced by the solar day. For some, particularly those living in or near the intertidal zone, the rhythms of the tides and moon can be at least as great an influence. Some lifestyles even depend upon the interaction between these two rhythms as, for example, some marine animals that lay their eggs at the high-water mark of one Spring tide and whose newly-hatched offspring are swept into the sea by the next (Palmer, 1976; Saunders, 1977). As a result of this all-pervasive rhythmicity in our environment, the observation that physiological and psychological variables show daily (24 hr) rhythms for terrestrial organisms and lunar (24.8 hr) rhythms for some marine ones comes as no surprise. Some examples, chosen almost at random from the gamut of rhythms in humans, are shown in Fig. 1. It is important here to recognize two general features. First, there is a day-to-day reproducibility of

such rhythms (in healthy subjects living a normal lifestyle) with regard to (i) their period--the time it takes for one cycle to be completed, (ii) their general shape and (iii) their timing (phase). Secondly, it is evident that different rhythms, even though they all show a 24 hr period, will also have characteristic shapes and phases. Rhythms with periods different from 24 hr have been described (1 year, 1 month, 1 week and 1-2 hr, for example) all of which may prove to have a significant influence on pharmacological responses. (Rhythms with a period of less than 20 hr are described as ultradian, a subset of which, with periods in the order of an hour, being known as circhoral; rhythms with periods longer than 28 hr can be described as infradian.) However, this review will concentrate on circadian rhythms, those with a period of about a day. In seeking the cause of such circadian rhythms, it might be suggested that they are most obviously a direct reflection of our daily habits and environment, with activity, light, noise and food intake during the day-time and fasting, sleep, quiet and dark at night. This is not wholly the case, however; adaptation of an organism to its rhythmic environment is far more finely tuned than being merely a response to it. Close inspection of the data of Fig. 1 will indicate that body temperature falls in the evening before sleep onset and begins to rise while we are still asleep, and that urinary potassium excretion decreases in the evening in spite of having eaten late in the day. More generally, the anticipatory activity of many animals just before their feeding time is well known. These results suggest that some factor other than our lifestyle and environment is exerting an effect. What this other factor might be can be observed more clearly in humans undergoing a Constant Routine protocol (Minors and Waterhouse, 1984). In this, subjects are required to stay awake and either recumbent or seated for at least 24 hr. During this time they are in an environment in which noise level, lighting, temperature and humidity are all held constant. Subjects are also required to take regular identical snacks, the composition of which is such that the total daily intake is as normal as possible. On such a constant routine, rhythmic inputs from the environment and lifestyle have been effectively removed. As an example, the results shown in Fig. 2 demonstrate what happens to the rhythm of body temperature under these conditions. The results show three important features. (1) The rhythm continues, albeit with a diminished amplitude. This rhythm must originate from inside the subject; it is therefore called the endogenous component of a rhythm and is attributed to an internal 'clock'. (2) The amplitude of the rhythm is less, and this is because rhythmic changes in the environment and lifestyle are missing; these influences are collectively called the exogenous component of a rhythm. (3) The two components---endogenous and exogenous-are normally in phase. That is, the internal 'clock', and our activities and environment both raise body temperature in the day-time and lower it at night.

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FIG. I. A selection of circadian rhythms measured in healthy subjects living on a conventional sleep/activity (sleep 0000-4)800). 11-OHCS = 1l-hydroxycorticosteroids. These findings apply in general to all variables and organisms. However, there are differences resulting from differences in (i) the relative importance of the endogenous and exogenous components of a rhythm, (ii) the factors that give rise to the exogenous component, and (iii) the phase of the rhythm--for instance, the contrast between behavioral rhythms and the environment in diurnal and nocturnal species is particularly marked in this respect. For the chronobiologist it is the endogenous component of a rhythm--the internal 'clock'--that is of most interest. More detailed study of this requires a longer period of time than the 24-48 hr that is feasible in a constant routine. However, even with subject compliance, studies that are much longer than 24 hr will begin to be dominated by the effects of sleep loss rather than those due to an internal clock. A different

protocol is required, that of the free-running experiment. In such a protocol the organism is placed in a time-free environment i.e. one in which light, temperature, humidity and noise are maintained constant and attention from the experimenters (cleaning cages, providing food and water) is given at random times. Physiological considerations often dictate that experiments upon plants must be performed in constant light whereas, for noctural rodents for example, constant dim light ('darkness') is used. With human volunteers the tendency has been to allow them to control their own light/clark cycle, in the absence of any external clock or other time-cues, and to be active in the light and to sleep in the dark. For animals and plants, the provision of a time-free laboratory has not proved difficult, but the size of a human, together

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FIG. 2. The body temperature rhythm of a group of subjects measured: (full line), on a conventional sleep/activity schedule; (dashed line), during constant conditions. Reprinted from Minors and Waterhouse (1981) with permission of the copyright holder, Wright PSG, Bristol. with his great social awareness and inquisitiveness, has meant that the problem of finding a time-free environment has been a more severe one. In practice, three environments have been used: the Arctic during the constant light of summer; underground caves; and specially-constructed isolation chambers. Fortunately, the results obtained from humans do not appear to depend upon which of these three environments is chosen (Wever, 1979). An example of the kind of result that is obtained is shown in Fig. 3, from which it is clear that rhythmicity does not disappear, whether the rhythms of temperature or sleep/activity are considered. Moreover, when other rhythms are measured, these too continue. The continuation of rhythms (with a period deviating from exactly 24 hr) in the free-running experiment is powerful evidence in favor of there being an internal, self-sustaining clock, particularly when the reproducibility of the result is considered (Fig. 3). The result does raise what appears t o be a fundamental problem, however--the internal clock is a poor timekeeper! In recognition of this it is called circadian (circa, about; dies, a day), though, perhaps confusingly, this term is used--as above--to describe any rhythm with a period in the range 20-28 hr, whatever the circumstances under which it is measured. Humans show a free-running period of about 25.0 hr on average (Wever, 1979); other species show free-running periods that are above or below 24 hr. For example squirrel monkeys have a mean free-running period similar to that of humans, whereas golden hamsters have a period of about 23 hr (Moore-Ede et al., 1982; Palmer, 1976; Saunders,

1977); so far no convincing explanation of why some species' clocks run slow and others fast, has been found. Whatever the explanation, some means of adjustment of the clock to the required period (24.0 hr solar day) is required. The process is called synchronization or entrainment and the factors that bring this about are called zeitgebers (Zeit, time; geber, to give). Zeitgebers are rhythmic changes in the environment and their nature depends upon the organism. Thus, for plants it is the alteration of light and dark that keeps the internal clock and the solar day in step (Palmer, 1976). For a newborn and unweaned mouse pup it is the presence of its mother--to enable it to suckle--that is the entraining agent, while for many predatory creatures it is likely to be the availability or otherwise of a potential food supply and sufficient daylight to allow hunting. When humans are considered, it is probably the totality of our environment and lifestyle--rhythmic changes in social factors, lighting, feeding and act i v i t y - t h a t produces entrainment. Furthermore, the several factors are likely to be interdependent. Thus our sleep/activity rhythm will automatically influence our social rhythms, which in turn will affect (or even overlap with) rhythms in eating, activity and exposure to light, particularly sunlight. It is coherence between potential zeitgebers that acts as a powerful force to adjust our clock; equally, during shiftwork, when there might be a clash between rival zeitgebers, problems of adjustment of circadian rhythms are known to arise. Under normal circumstance, however, zeitgebers synchronize the environment, our

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FIG. 3. Above, alternation between activity and sleep (bars) and the rhythm of rectal temperature (triangles). Below, average cycles (with standard deviations) of the temperature rhythm. The two sets of data, which were separated by a gap of one year, were obtained from the same individual. Adapted from Wever, 1983, with permission of the author and the copyright holder, Boxwood Press, Pacific Grove. lifestyle and internal clock. If our clock is running slightly late, then the combination of an alarm clock and the morning rush will tend to advance it; if our internal clock is preparing us for sleep too early then it will be delayed by evening events. Possession of an internal clock---even a clock which is apparently not capable of maintaining a period of 24 hr without constant adjustment----confers a powerful attribute on the organism; this is the ability to predict routine changes in the daily environment. Thus in the human, blood pressure (Floras et al., 1987; Millar-Craig et al., 1987) and plasma cortisol (Kreiger, 1979) begin to rise sharply during the latter part of the sleep period, examples of physiology and biochemistry toning up for the rigors ahead. Conversely, at the end of the activity span, the individual can also prepare for sleely--it is a common experience that we cannot sleep if our minds are too active. To distinguish these preparations for the environment from the more conventional reflex changes initiated by it ('reactive homeostasis'), Moore-Ede (1986) has described them as examples of 'predictive homeostasis'. Differences between the timing and shapes of rhythms in an individual have already been described. Differences exist also between individuals. The best studied example is the group of related circadian

315

rhythms of sleep times, day-time alertness and performance of some simple mental tasks. In most individuals the peak of the latter two rhythms is positioned mid- to late-afternoon (Folkard and Monk, 1986), but about 10% of the population show rhythms that are phased earlier than average by about 2 hr, and at the other extreme of the population is another similarly sized cohort who show the opposite shift, their rhythms being delayed (Kerkhof, 1985). The groups are known as morning types ('larks') and evening types ('owls') respectively. There are two types of possible cause for these rather extreme phases. The first is 'endogenous' insofar as the phase of the rhythm is a reflection of an internal clock that runs slightly faster (morning types) or slower than average; there has been no systematic test for such a hypothesis. The second is 'exogenous' in that it postulates that zeitgebers were initially phased earlier than usual (in the case of morning types) and that they become habits in due course. Continuing to rise early during retirement--because of a habit acquired during one's working life---is an obvious example. It must be remembered, however, that, accepting the interaction between 'exogenous' and 'endogenous' factors--a necessary consequence of the role of zeitgebers--an explanation of morning and evening types in terms of a single factor is probably simplistic. It is likely that an individual with a 'lark-like' clock, for example, will attempt to organize his lifestyle to stress morning rather than evening activities; in so doing the tendency to be a lark is reinforced. An opposite scenario for 'owls', in which slightly delayed clocks and habits interact, is equally easy to imagine.

3. OPENING THE BOX--ATTEMPTS TO DESCRIBE THE DETAILS OF CIRCADIAN RHYTHMS The position described so far can be summarized by the diagram shown in Fig. 4. It emphasizes the dual role of the environment (as a zeitgeber and exogenous influence) as well as the possible lack of identity between the measured rhythm and the output from the internal clock. We will now consider some details of the system that might be of particular interest to pharmacologists and neurochemists. 3 . 1 . EFFECTOR MECHANISMS---CHANGES IN HOMEOSTATIC 'SET-POINTS'

The means by which the body clock might produce rhythms in humans' physiological systems has been studied in particular by Cabanac's group and others investigating temperature regulation (Cabanac et al., 1976; Marotte and Timbal, 1982; Terai et al., 1985). They showed, first, that if a subject's body temperature has been raised above the set-point then he would feel more comfortable if his hand were placed in cool, rather than warm, water. By contrast, with his body temperature below the set-point, he would prefer his hand in warm water. If the body temperature of an individual is lowered then raised (by placing him in cool, then warm, water) repeated

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In summary, there are circadian changes in reflex pathways which lead to changes in the set-point in the homeostatic system of which the pathway is part. The means by which such changes in the reflex pathways might arise needs consideration. 3.2. CIRCADIAN RHYTHMS IN PATHWAYS

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1 7 °°'°' FIG. 4. The environment as a zeitgeber and the exogenous component of a circadian rhythm. testing of the preferred temperature of the individual as his body temperature is raised from the subnormal value gives an estimate of his thermoregulatory setpoint at that moment. One of the findings with this method was that there was a circadian rhythm in the set-point, this being a lower value at night, rising during the morning to a maximum in the afternoon, and then falling again in the evening. (This is very close to the body temperature rhythm itself, see Fig. 1, and stresses how effective the homeostatic control of body temperature normally is.) Since thermoregulation is achieved by an interaction betweeen heatgaining and heat-losing reflexes, changes in the set-point imply that the thresholds and sensitivities of these reflexes change during the course of each 24 hr day (Engelberg, 1966). Recent work has substantiated this view (Marotte and Timbal, 1982; Stephenson et al., 1984; Terai et al., 1985). Figure 5 shows the stimulus-response curves for sweating at two different times of the day; clearly a change in threshold has taken place. Therefore in the evening, when the thresholds for cutaneous vasodilatation and sweating fall, heat loss is more likely to take place and body temperature will be controlled at a lower value (that is, the 'set-point' will be lowered). The opposite changes occur in the morning with body temperature tending to fall below the rising set-point. A further implication of these results is that during the evening, with body temperature tending to be above the 'set-point', a cooler ambient temperature will be preferred and during the hours around waking, a warmer environment (Cabanac et al., 1976; Terai et al., 1985). Circadian changes in reflex activity have also been described for humans and other mammals in the urinary response to water loading (Kass et al., 1980), the orthostatic response to postural changes (Aschoff and Aschoff, 1969), and in the endocrine response to controlled hemorrhage (Engelund et al., 1985). It has also been known for some years that the sensitivity of reflex pathways shows circadian variation. Examples are the response of the adrenal glands to pulses of ACTH and corticotrophinreleasing hormone (De Cherney et al., 1985), and the suppression of the hypothalamo-pituitary-

Figure 4 indicated that a protocol which maintains an individual in a constant environment and with constant habits will remove, from a measured rhythm, the rhythmic input produced by the exogenous component. The rhythmicity that remains is attributed to the endogenous component of the rhythm (see Section 1). On first consideration it might be assumed that this is identical to the output from the internal dock; this is almost certainly not so. The rhythm that is measured will be linked to the internal clock by a pathway that will contain several (the exact number is unlikely to be known) synapses. Inherent in synaptic mechanisms are various ways of integrating information, the outcome of which is that the inputs and outputs of synapses are different. There is increasing evidence that many of the elements of synaptic function which make integration possible display circadian variation. Thus there are examples of circadian rhythms in the rate of precursor uptake into neurons (Loizou and Redfern, 1988), and the rate of transmitter synthesis (Hery et al., 1972) and of transmitter release (Faradji et al., 1983). Similarly, the number of postsynaptic receptors can be shown to vary over 24 hr (Campbell et al., 1985), as can the response to pharmacological stimulation of specific receptor populations (Moser and Redfern, 1984). These processes of neuromodulation and up- or down-regulation of receptors may alter the input-output relationship at each synaptic link. The particular relevance of this to the present discussion is that they could be expected to affect the amplitude or phase, but not frequency, of circadian rhythms. For example, in the rat the rate of release of 5-hydroxytryptamine (5-HT) from central synapses apparently displays a circadian rhythm with greater release during the dark (active) phase (Faradji et al.,

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Circadian rhythms 1983). Behavioral and biochemical evidence suggests that populations of 5-HT2 receptors within the brain also exhibit circadian variation but that 5-HT1 receptors do not (Moser and Redfern, 1984). The phase relationship between the reported rhythm of 5-HT release and that of 5-HT: receptor number is such that at the time of day when transmitter release is greatest, receptor response is lowest, with the result that the amplitude of any circadian rhythm 'downstream' from the 5-HT 2 receptors will effectively be damped (Moser and Redfern, 1988). In contrast, functions dependent on activation of the apparently arrhythmic 5-HT~ receptors will not be subject to any such damping. It is thus possible to postulate an important role for synaptic modulation as an intermediate step between the endogenous clock and the expressed- and measured-rhythm. Not surprisingly, drugs that affect specific elements of synaptic function can be shown to alter the amplitude and phase of the circadian rhythm exhibited by the synapses and by behavioral elements dependent upon them (Martin and Redfern, 1985, 1987) but it will be clear from the foregoing argument that it cannot be inferred from these altered rhythms that the endogenous clock has been directly affected. Zeitgebers are the means by which the environment can exert an effect upon the phase of the internal clock and intensive investigations of the mechanisms involved have been carried out recently. It seems well established, in several species including man, that a direct connection between the retina and suprachiasmatic nuclei (SCN) of the hypothalamus exists (Brandenberg et al., 1981; Dadun et al., 1984; Turek, 1985). This retinohypothalamic tract is supposed to be the means by which the light/dark cycle acts as a zeitgeber. (The evidence that the SCN function as the clock is given below.) Input pathways for social, activity and feeding rhythms, all of which might contribute to the 'zeitgeber package', are less well understood, though there seems to be no lack of neuronal input pathways that might be important (Meijer and Rietveld, 1989). Neuromodulators and other hormonal factors borne in blood or CSF must also be considered. Just as light can adjust the phase of the internal clock so also can several transmitters, receptor agonists and antagonists, substances that modify protein synthesis or membrane function in general, drugs that are believed to react specifically with receptors in the SCN, and substances such as K + and tetrodotoxin that modify axonal activity in general (Meijer and Rietveld, 1989; Turek, 1985). It will need painstaking research to produce from what is presently an incomplete collection of disparate data some model to describe how zeitgebers adjust the internal clock. A clear understanding of the neurochemistry and neurobiology of this model is a prerequisite of rational pharmacological intervention. 3.3. THE INTERNALCLOCK A direct measurement of the internal clock would appear to be a means of overcoming this dilemma; but this aim is soon thwarted and not only because of technical difficulties. The evidence relating to the position of the clock in mammals is complex and

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has been summarized elsewhere (M. H. Hastings, manuscript in preparation; Meijer and Rietveld, 1989; Minors and Waterhouse, 1986; Moore-Ede, 1983; Ralph et al., 1990; Rosenwasser and Adler, 1986; Rusak, 1989; Rusak and Zucker, 1979). In briefest outline, techniques involving recording of electrical and chemical activity in vivo and in vitro, and recording behavioral activity after selective ablation of areas of the brain, have focused attention on the paired hypothalamic SCN. Such a position for the clock would have the advantage that, as has already been alluded to, neural inputs exist from the retina (the retinohypothalamic tract), raphe nuclei and many other regions of the brain which would enable potential zeitgebers to gain access to, and so entrain, the internal clock. It would also locate the neural mechanisms responsible for control of 'predictive homeostasis' within the hypothalamus and therefore immediately adjacent to neural mechanisms controlling 'reactive homeostasis'. Recently, however, the picture has become complicated by a series of results (referred to in the reviews cited above) that indicate the need for more than one internal clock. In this regard claims have been made for a timekeeping role for the pineal gland (Binkley, 1982), for an area in the ventro-lateral hypothalamus (Moore-Ede, 1983) and the intergeniculate leaflet of the thalamus (Meijer and Rietveld, 1989). The results on which these claims are based include the following (though some of them are open to dispute): (1) Humans in time-free experiments can show spontaneous internal desynchronization, in which rhythms with two periods are seen simultaneously (Wever, 1979). This phenomenon is very rare in other animals but 'splitting'--the development of two bursts of activity, one corresponding to the light/dark transition and the other to the dark/light transition-is not uncommon (Moore-Ede et al., 1982; Palmer, 1976; Saunders, 1977). (2) SCN ablation does not result in the loss of all rhythmicity; activity and drinking might become arrhythmic or show instead ultradian rhythms (rhythms with a period of less than 12hr), for example, but the body temperature rhythm might continue to show circadian rhythmicity, albeit less strongly (Moore, 1983; Moore-Ede, 1983; Turek, 1985). The source of this remaining circadian rhythmicity is believed to be part of the ventro-lateral area of the hypothalamus. (3) In passerine birds and other species, the pineal gland has a claim to be an autonomous clock that is as strong as the claims made for the SCN (Binkley, 1982). Whether two (or even more) clocks really exist in the brain and whether or not they are even needed are issues that still need resolution. However, the observations (see, Meijer and Rietveld, 1989; Redfern et al., 1985)--that (1) the SCN send outputs to many areas including the ventro-lateral hypothalamus and (via the sympathetic nervous system) to the pineal and (2) there are melatonin receptors (and receptors for other neuropeptides) in the SCN--all suggest that the concept of a single circumscribed area of the brain acting as the internal clock needs modification.

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One solution is to suggest that the timekeeping role is normally shared by two or more structures which individually influence different variables to different extents. Normally these two (or more) structures, or clocks, are synchronized, but certain experimental circumstances result in the effect of the different structures becoming separated functionally (desynchronization) or even for one of them to cease to function entirely (for instance as a result of ablation). This hypothesis could account for many of the above observations though it implies that the original idea--that of recording directly activity from the site of the internal clock--is no longer meaningful. However, it does open the way for neuropharmacological and neurochemical studies of the interactive processes that would be implied by such a model. The concept of an internal timing system deriving from more than one site raises the possibility of redundancy in the system which itself can lead to interpretive problems. By analogy, consider the control of movement by the brain. It is problematical to ask where movement originates in the brain since it requries the integrated response of several areas. Moreover, movements continue to be made when 'important' areas have been removed because of redundancy in the system and plasticity of the brain. If the timing system conforms to this analogy, then there might be severe limitations to the interpretations of the results of many experiments that are based so firmly on a reductionist approach and assumptions about an immutability of function of specific brain areas. Redundancy exists also when it is realized that individual cells, tissues and organs throughout the body show rudimentary circadian rhythms (see Moore-Ede et al., 1982, for review). This is perhaps less surprising when it is remembered that all animal and plant species--including unicellular algae and protozoans--show circadian rhythms (Palmer, 1976; Saunders, 1977). In mammalian systems this fact is incorporated into the general scheme by postulating some form of hierarchy between all the circadian clocks (Moore-Ede, 1983). At the top of this is the 'master oscillator' which, as just discussed, might itself be more appropriately considered as being composed of more than one part. The role of the master oscillator is to impart temporal information to all the subsidiary circadian clocks (in effect, it takes on the role of an 'internal zeitgeber'). The means by which this information is transmitted down the hierarchy could be via circadian rhythms in body temperature, hormones or the autonomic nervous systems, all examples of rhythms that permeate the whole body (M. H. Hastings, manuscript in preparation). The view that cancerous cells grow uncontrollably because they are no longer governed by normal cellular mechanisms receives support from the hypothesis just described; thus carcinomatous breasts are observed not to show circadian rhythms of temperature, unlike contralateral controls, as if their circadian clocks were no longer controlled by the master oscillator (Simpson, 1978). 3.4. INSmE THE SCN When the detailed mode of action of the cells in the SCN is considered, an important consideration is

whether the individual cells behave as a series of identical clocks or whether their integrated output is different from those of the constituents (see, for example, Fig. 10c below and associated text, and Enright, 1989; Jacklet, 1978, 1985; Meijer and Rietveld, 1989; Turek, 1985). By way of an analogy, consider a mechanical clock which works because of a device (the escapement) that regulates the release of energy from a wound spring. The energy is used to turn a series of intermeshing cogwheels. The output is chosen to show the passage of time at a convenient rate. We might even choose more than one output from the same device (taken from different cogs)-say, indications of the passage of a second, minute, hour, 24-hr day, or 29.5-day lunar month. In attempting to understand how the clock worked, one experimental approach would direct our attention to the individual cogs and their structure and properties. We need to have such information about the parts of the clock but we also need to know how the components interact. The clock is not the sum of its components; it is the result of their interaction. In the same way, even though we need to know much more about the neuroanatomy, neurochemistry, neurophysiology and neuropharmacology of the constituents of the body's timing system, we might also need to know how these constituents interact and what is the consequence of this interaction to the system as a whole. The 'black box' model (Fig. 4) is useful as a concept but it might have limitations and even be frankly misleading if it is regarded as having a clear and immutable anatomical counterpart. Further work will investigate in more detail the anatomical structures and their biochemical interconnections with each other--but only time will tell if this reductionist approach is sufficient or whether some additional holistic description is required.

4. COLLECTING DATA FOR CIRCADIAN RHYTHM STUDIES Intuitively, if we are to study and fully characterize circadian rhythms, we will need to collect data as frequently as possible over at least a 24 hr period. Is this intuition correct and, if so, how frequently must we collect data? 4.1. FREQUENCYOF SAMPLING Constraints imposed by finance, time and ethics may limit the number of experiments that one wishes to perform. However, a restriction in the frequency of sampling can influence considerably the inference that can be drawn from a set of results. Consider, for example, the data of Fig. 6. Figure 6a shows concentration of plasma cortisol recorded at half-hourly intervals throughout a single 24 hr period. The same data are then replotted in Figs 6B-F as they would have been recorded with less frequent sampling. With hourly sampling (Fig. 6B), short-lived peaks or pulses are lost (consider the first part of sleep, for example), and, with 2 hr sampling (Figs 6C and 6D), only the major peaks are present. With 4 hr sampling (Figs 6E and 6F), only the general nature of the rhythm is

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preserved; the number and size of peaks and their timing can be described only approximately. Analysis of cortisol in urine effectively provides an integrated sample (the mean of values since the last collection time) and would give the result shown in Fig. 6G if samples were collected every 2 hr. (In deriving these results the assumption has been made that plasma and urine concentrations at any moment are identical.) In practice, urine sampling is often less frequent and only a single overnight sample is collected on rising (Fig. 6H). Whilst this early morning sample gives information gained from the whole night--and so differs from a 'point' sample taken at the same time (heart rate for example), it cannot give information about changes during the night. The fact that the rise in cortisot occurred in the second half of thg night is completely lost. An implication of this is that, when rapid fluctuations in concentration are expected, as during the night and in the hours around waking in the case of plasma cortisol, frequent sampling is most important if an accurate picture is required. By contrast, during the late afternoon and evening, when changes are smaller and less erratic, infrequent sampling is less likely to produce misleading results. 4.2.

COMBINING AND SMOOTHING RESULTS

In nearly all experimental work, results are combined or averaged in some way. This might entail combining data from repeated samples from an individual, or pooling data from a group of subjects or pieces of tissue. A common example in chronobiology is to sample from different groups at different times during the 24 hr. Often this is the only way in which points covering the 24 hr can be obtained. However, such processes are not without their problems when applied to circadian rhythm studies. First, the different tissues or animals must be in phase with one another. This is generally achieved by exposing the experimental animals to the same zeitgebers. Failure to achieve such synchrony will tend to broaden the timing of any peaks and troughs and reduce the amplitude in grouped data. In the extreme situation of a completely desynchronized population, the combined output could be arrhythmic in spite of the individual components (be they cells or whole animals) showing marked rhythms. A second problem is that the variable under consideration must show the same 24 hr mean value and amplitude in the different animals or tissues. Figure 7 shows the simple example of rhythms from three animals (results from which are indicated by curves a-c) that have the same amplitude and phase but different mean values. Each animal is sampled only at 6 hr intervals, but, by staggering the sampling by 2 hr, a 2 hr sampling frequency for the group as a whole is achieved. The shape of this grouped result (Fig. 7) bears no obvious relationship to those of the individuals; indeed the experimenter would be likely to draw the inference that a rhythm with a period of about 6 hr was present in the results. This artifact will not be produced if the means and phases of individuals can be corrected for by 'standardizing' results from them. This often consists of expressing the results in terms of the percentage of the 24 hr mean, a method

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5. ASSESSING RHYTHMS WITH A 24 hr PERIOD A rhythm can be described in terms of four parameters: (i) the period--the time it takes for one cycle to be completed and for the pattern to repeat itself; (ii) the mean--the average of all points within a single cycle; (iii) the amplitude--the maximum deviation of the rhythm from its mean, and (iv) the phase---the timing of the rhythm with reference to some external standard. This latter is often expressed as the time of the peak value with respect to local midnight or the time of the minimum with respect to midsleep. Mathematical techniques exist for estimating these parameters, but the methods demand far longer spans of data and higher sampling frequencies if the period of the data is being sought. These well-tried and tested methods, many of which were originally designed for use in the physical sciences, are reviewed elsewhere (Minors and Waterhouse, 1988, 1989) but are beyond the scope of this article. The position is simplified if the period within the data is known or can be assumed--for instance, in the present context, a value of 24.0 hr. In practice, this assumption can be made when studies are performed upon animals or human subjects that have been living in a normal (24.0 hr) environment for at least several days beforehand; however, Enright (1989) has recently stressed the errors of interpretation that can arise if this assumption is unwarranted. Assuming that any rhythmicity that is present has a period of 24 hr, then two methods are commonly used to assess it.

analysis, even if it establishes that rhythmicity exists, does not give information as to its shape, amplitude, mean or phase. (It is most unlikely anyway that, with only a few sampling times, those corresponding to times of maximum and minimum would have been chosen or that the mean of the samples would represent the true mean of the underlying rhythm.) 5.2. COSINOR ANALYSIS

Cosinor analysis, probably the most enthusiastically promoted method, has been fully described elsewhere (Nelson et al., 1979). Briefly, it involves representing the data span by the best-fitting cosine function of the form: Yt = M + A cos(coti + 4') + e i .

(1)

where Yi = the value of the i-th point in the data span; t~ = time when this point was measured; M = the mean level (termed mesor) of the cosine curve; A = the amplitude of the curve; o~ = angular frequency of the curve; 4' = phase angle of the maximum value (termed acrophase) of the curve; e~= residual error of the i-th point, assumed to have a mean value of zero when all timepoints are considered. Equation (1) may be expressed as: Yi = M + flXli ~- ?X2i -~- e~

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5.1. ANALYSIS OF VARIANCE

A fairly simple method is a one-factor (time of day) analysis of variance (ANOVA). This assesses whether the variance between time points is significantly greater than the random variation within them. The analysis requires several readings to be taken at each of a group of times within the day; the times of assessment do not have to be evenly spaced. The statistical tests are more likely to establish the presence of a time-of-day effect as the number of groups (time points) and the number of values within each group increases. ANOVA tests exist that deal with matched and unmatched data as well as with parametric and nonparametric measurements. (Strictly speaking, nonparametric tests should be used with data that have been standardized by expressing them as a percentage of the 24 hr mean, see above.) Although clearly difficult to achieve in practice, a statistically powerful design is when the same subject or animal is assessed at different times of day, because the matched data reduce interindividual variation. A strength of ANOVA methods is that the shape of the rhythm does not affect the statistical outcome. Thus, the sequence of time-points could be interchanged without statistical effect, even though the biological implication might be considerable. Such an

7 = - A -sin 4'. Values for the parameters fl and y can be derived from the data by conventional methods of leastsquares regression analysis and from these can be estimated the amplitude, mesor and acrophase. Cosinor analysis is a very powerful technique, because it can deal with irregular sampling, with integrated (for example, urine samples) as well as point (for example, blood samples) data, and it can also estimate confidence intervals for the mesor, amplitude and acrophase. Moreover, cosine curves describing a whole group or a population of individuals over several days can be calculated (Nelson et aL, 1979). Cosinor analysis is an objective assessment of all the data span. In this respect it might have advantages over methods which assess only maximum or minimum values, which are prone to the effects of a single aberrant value. From a statistical viewpoint, Cosinor analysis simply investigates if the data are better described by a cosine curve than by a straight line. A 'significant' fit (p < 0.05) is taken as one where the chance that the data are fitted as well by a horizontal line as by the cosine curve is < 5%. (This decision is based upon a comparison of variances-the variance of the data about the fitted cosine curve and the variance of the fitted cosine curve about its

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mean or mesor.) A significant fit is alternatively described as one in which the amplitude of the fitted curve is significantly different from zero. It is sometimes informative to assess the percentage of variability in the data that is accounted for by the fitted curve; this is the 'percentage rhythm'. To calculate this, a direct comparison is made between the variability of the data points about the fitted curve (the summed squared deviations from the curve, that is, the residual sum of squares, RSS) and the total variability present (summed squared deviations about the mean, that is, the total sum of squares, TSS). The percentage rhythm can be calculated as: Percentage r h y t h m = 1 0 0 x ( T S S Z s R S S ).

(3)

A perfect fit would give a value of 100%, because RSS would equal zero. What assumptions does a Cosinor analysis make, and what difficulties of interpretation exist with this method? First, the lack of a 'significant' fit does not indicate necessarily that a rhythm is absent (see also Section 5.3.1). Thus a major assumption of the analysis is that the data are approximately sinusoidal in shape, an assumption that is sometimes obviously untrue. Circadian rhythms vary greatly in their shape, and for a particular variable that shape might be distincitve. The example of plasma cortisol has already been given (Fig. 6). Another fairly common shape (Fig. 8A) is the 'saw-tooth' which rises steadily through the day and then falls more quickly during the night; blood urea nitrogen concentration approximates to this (Conroy and Mills, 1970). Another shape that is not uncommon is a 'square wave' (Fig. 8B), when there is alternation between two states or values, as for example between activity and sleep. Rhythms with a shape closely approximating a cosine curve are not common, though plasma phosphate on a constant diet and deep body temperature during free-running conditions are examples (Conroy and Mills, 1970; Moore-Ede et al., 1982; Wever, 1979). Given the wide variety in the shape of measured rhythms, and the relative variety of data closely approximating to a sinusoid, one might legitimately question the validity of results obtained by Cosinor

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Often we wish to know if a rhythm has changed in response either to some experimental manipulation, say a simulated time-zone transition, or to the administration of a drug or as a result of some illness. Interest often centers on the loss of a significant fit to the data by a cosine curve or the shift in acrophase of the curve. Either result is associated with some interpretive problems that require comment. 5.3.1. Change of Amplitude

FIG. 8. Different shapes of circadian rhythm. A. 'saw-tooth'; B. square-wave; C. 'ramp' function. In each case, two full cycles are shown. Reprinted from Minors and Waterhouse (1988) with permission of the copyright holder, Pergamon Press, Oxford.

A loss of amplitude implies that a cosine curve no longer fits the data span better than a straight line. This is interesting, in itself, of course, but there are several possible means of obtaining such a result, as summarized graphically in Fig. 10. It is important to realize that rather different inferences can be drawn from each possibility and that visual inspection of the

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Flo. 10. Possible ways (a-d) in which circadian rhythmicity (control) can be lost after experimental manipulation (for details see text). Reprinted from Minors and Waterhouse (1988) with permission of the copyright holder, Pergamon Press, Oxford. data will often help to distinguish between them. Thus case 'a' implies that some mechanism is setting the variable at a maximum value (as would be the case with the effects of maximal sympathetic stimulation upon bronchial dilatation). Case 'd' is similar except that there is a maximal inhibition (as might occur with bright light and melatonin secretion). In case 'b' there is the implication that the control rhythm was due to both increases and decreases about some tonic value. (Note also that cases 'a', 'b' and 'd' are very similar to those producing curve 1, in Fig. 12. see below.) Finally, case 'c' implies the loss of some means of coordinating more rapid ultradian rhythms into a circadian whole. If the experiment has been performed on pooled data, then the possibility of desynchronization exists and should be eliminated as a possible cause of the fall in amplitude. For example, if the experimental manipulation removes zeitgebers and so prevents the internal clock from being synchronized, then the individuals in a group of animals will gradually lose their synchrony with each other. As a result, the combined rhythm will decrease in amplitude and become statistically nonsignificant. In such a case, inspection of continuous data from several individuals would show in each a rhythm of unchanged amplitude but with a slightly different free-running period. If the data have been obtained by pooling single samples from different animals (see Fig. 7 for example), then there is no easy way to establish if the animals are either arrhythmic or rhythmic but asynchronous. The continuous measurement of some other rhythm might be a useful means of distinction. 5.3.2. Change in Acrophase A difference in acrophase cannot automatically be considered as an accurate measure of the amount by which a rhythm's phase is shifted. The shift in acrophase will be an accurate measure of the shift in rhythm if the shape of the two sets of data are the same. For example, Fig. 11 shows sets of data which show acrophase changes, but only in the second example is the shift not produced by a change in shape. There are three common reasons why a rhythm changes shape. The first is because the overt circadian rhythm is the sum of exogenous and endogenous components (Fig. 4) and so, after a shift of lifestyle as, for example, occurs after a time-zone transition, there

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FIG. 11. Effect of changes in shape of data upon estimated acrophase, T. might be a temporary loss of the normal matching between the two components. The result would be that, even though the shape of the components had not changed, that of the combination would. A second cause is a change in the shape of the exogenous component. This is possible because it is produced by the environment and by the behavior of the organism; it will be noted that this would be an example of 'masking' of the endogenous component of a rhythm, and a constant routine would enable any shift of the body clock to be assessed specifically. The third possibility is that the change in shape is caused by artifacts of inadequate sampling frequency. This is illustrated by comparing the shapes of Figs 6A-E. It is important to realize that the apparent shifts seen in Figs 6D and 6F--and of a type often measured experimentally---can lead to marked difficulties in interpretation. 5.4. ALTERNATIVESTO THE SINGLE COSINE CURVE The observation that data often deviate from a sinusoidal rhythm has led to alternative mathematical description of data spans. Some possibilities are outlined below.

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One method is to use a model which is a summation of the fundamental period of a cosine curve and various harmonics. For example, 12 hr, 8 hr, 6 hr periodicities etc., can be added to the basic cosine curve with a period equal to 24 hr. This method has been used by Van Cauter to describe the circadian rhythm of plasma cortisol, for example (Van Cauter, 1989). However, the procedure of adding harmonics to the fundamental period raises a general point with regard to the use of mathematics in biological systems. Increasing mathematical complexity undoubtedly results in the experimental data being better described mathematically; however, the physiological, biochemical and histological interpretation of such models is often very difficult. There is a very real danger that the biological importance of the rhythm becomes obscured by a complex of mathematical equations. A different approach which avoids this problem is to consider the biological concepts first and then to base a mathematical model upon them (Minors and Waterhouse, 1987, 1991). One example of this would be to describe the value of a variable, Y at time T as: Yr = (Endogenous Component)r + (Exogenous component)r... + Errorr.

(4)

The endogenous component is approximated by a cosine curve (see Fig. 2, the endogenous component during the constant routine) and has the mathematical form shown in Section 5.3, eqn 1. The exogenous component will depend upon the process(es) believed to cause it. Thus it might be a function of: (1) time elapsed since last meal (as might be the case for plasma insulin), (2) roughness of the sea (energy expenditure in pelagic fish), (3) time elapsed since last sleep (some forms of mental performance), (4) activity (see exogenous component of Fig. 2, obtained by comparing the two curves). In each case, a mathematical term is required to describe the function. Quadratic or polynomial terms have been used but a simple yet versatile possibility is:

Exogenous component = B. TE c

(5)

where B and C are constants and TE = time elapsed. The value of C determines the general shape of the curve. Thus, with increasing values of TE, the function: decreases if C < 0, stays constant if C = 0, increases at a decreasing rate if 0 < C < 1, increases linearly if C = 1, increases at an increasing rate if C > 1. The best values for the parameters of the endogenous (eqn 1, Section 5.2) and exogenous (eqn 5) components can then be calculated if data exist which describe the variable (Yr) at known times of the day and after known amounts of time have elapsed since a particular event (TE). The best values will be those that minimize the value of the error term in eqn 4. This is generally assessed as the sum of the squares

of the differences between the data points and values predicted by the model. The important argument is that the mathematics have been the servant of the biological hypothesis, rather than vice versa; there is the advantage that a biological explanation for the results exists a priori. Even so, there are some difficulties associated with this approach. (i) A good mathematical fit to experimental results does not necessarily validate the biological model upon which the equation was based, because other models, based on different premises, might fit the data equally well. (ii) It might not always be possible to assess whether one particular set of parameters is, statistically, significantly better than another. (iii) If the fit to the data is poor, then a change in hypothesis (and type of mathematical function) is required, but the kind of change is not indicated by the model. 5.5. ASSESSING THE TIME OF MAXIMUM EFFECT OF AN EXPERIMENTAL PROCEDURE

In many pharmacological studies the experimenter may have little interest in describing the exact shape of the circadian rhythm of the variables under consideration but nonetheless might wish to know the time of day when a particular agent exerts its largest effect. :This can be difficult to decide if the control data, the background against which the effect is to be measured, are themselves rhythmic. Well-known examples where this difficulty has arisen include the effect of bronchodilators upon airway resistance in asthmatics, the effects of antihistamine drugs upon the responses to allergens, and the effect of agents that inhibit the release of antidiuretic hormone upon urine flow. Some of the possible results are illustrated in Fig. 12 which shows the circadian rhythm of a variable in the absence of any drug (control) and some possible responses after a drug has been added which raises the amount of the variable (curves 1-5). Possible interpretations of the results are: Curve 1. A maximum amount for the variable is reached under control conditions at time Y and the drug causes this maximum to be reached at all times. Curve 3. The effect of the drug is to raise the variable by a constant amount that is independent of the control rhythm. The means by which the drug acts and control rhythm is produced appear to be independent. Curve 4. The rise produced by the drug is proportional to the value of the control rhythm. This might indicate that the mechanism that is responsible for generating the control circadian rhythm is also responsible for a circadian sensitivity of the system to the drug. Curves 2 and 5. These are less straightforward, suggesting that changes in sensitivity to the drug exist but that, even though they show circadian changes, these are related to the mechanism producing the control rhythm (if they are related at all) in a complex way. Suppose that the time when the drug raises the level of the variable most is to be estimated. This requires

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